I don't think he was going to tell you.
Neither do I think that he has had sex with her just once.
I also think that regardless of what he says, he has been shifting the blame on to you.
Most people's response to wondering whether they were still loved would be to come home and thrash it out - not have an affair and dress it up as a cry for help, or to depict the OW as some kind of ministering nurse-maid.
I expect the truth of this is that he allowed a flirty friendship, thought he was entitled to a bit of fun while he was working so hard, didn't doubt your love or feelings for a second and thought that he could get away with it.
He probably thinks that with a toddler and a baby, you'll force yourself to accept it. He'll go back to the same job and remain in contact with the OW and eventually you will get over it.
You will never regret showing that he has sorely misjudged you.
So I would tell him you want to separate right now and put the onus on to him to take any action to protect his future fidelity. That means binning the lame excuses and admitting why he was really unfaithful. It also means changing his job and putting a stop to being a weekend/holiday husband and father. See what he does while he's apart from you and be slow to take him back.
If you try to accept what's happened and he does nothing but spout platitudes, he will learn nothing and will do this again to you.